Apple approved Steam Link for the App Store on May 7, only to reject it a couple of days later. Apple has not stated what motivated the change, but economics were probably a factor. Here’s Kyle Orland, writing for Ars Technica:

While the Steam Link app doesn’t have any built-in functionality allowing for direct game purchases, users can easily buy and download Steam games to the connected PC through the Big Picture mode interface while connected through the app. It’s plausible this functionality ran afoul of Apple’s guidelines, which require a 30-percent revenue share for any “in-app purchases.”